where \(\dot{N}\)  is the rate of neutrino events, \(\Omega \)  is the solid angle, \(E_\nu \)  is the neutrino energy, \(A_{\rm eff}(E_\nu , \Omega ^{\prime })\)  is the effective area of the IceCube detector and \(\Phi _\nu (E_\nu , \Omega ^{\prime })\)  is the signal neutrino flux. The effective area \(A_{\rm eff}(E_\nu , \Omega ^{\prime })\)  for full-sky shower-like event searches with the 79-string IceCube detector is provided by the IceCube Collaboration [1]}. In the case of null observation, the quasi-differential limit of the neutrino flux can be written as [2]}, [3]}
\(\Phi _\nu (E_\nu )=3\frac{N}{4\pi E_\nu T \log 10 \sum A_{\rm eff}(E_\nu )},\) 
